论文标题
Dirichlet到Neumann操作员的强制性以及对Muskat问题的应用
Coercivity of the Dirichlet-to-Neumann operator and applications to the Muskat problem
论文作者
论文摘要
我们考虑使用Lipschitz边界的Dirichlet到Neumann运算符。结果表明，由dirichlet to-neumann操作员生成的二次形式控制了一些尖锐的均匀分数Sobolev Norm。作为一种应用，我们证明了在\ cite {dgn}中为单相麝香问题构建的全球Lipschitz解决方案在任何Höldernorm $ c^α$，$α\ in（0，1）$中的及时逐步衰减。
We consider the Dirichlet-to-Neumann operator in strip-like and half-space domains with Lipschitz boundary. It is shown that the quadratic form generated by the Dirichlet-to-Neumann operator controls some sharp homogeneous fractional Sobolev norm. As an application, we prove that the global Lipschitz solutions constructed in \cite{DGN} for the one-phase Muskat problem decays exponentially in time in any Hölder norm $C^α$, $α\in (0, 1)$.
